FIG. 1 illustrates a schematic diagram of a capacitance variation detection circuit of a prior art described in Japanese Patent Public Disclosure (Kokai) No. 6-180336, to which a static capacitance of a sensor formed of a diaphragm and an electrode facing each other is connected. The static capacitance varies when the diaphragm moves in response to a physical pressure or the like applied thereto. The prior circuit shown in FIG. 1 has been proposed to solve a problem that a voltage applied to a sensor comprising a diaphragm and an electrode opposite thereto causes the electrode to come in contact with the diaphragm in response to an electrostatic attractive force, when the sensor is formed through fine machining on a semiconductor.
In FIG. 1, the reference numerals 1 and 2 designate voltage input and output terminals of the capacitance variation detection circuit, respectively. An input voltage Vin is supplied to the input terminal 1, and an output voltage Vout is output from the output terminal 2. The reference numerals 3 denotes an operational amplifier, 4 and 5 resistors, and 6 a switch. The input terminal 1 is connected to an inverting and non-inverting input terminals of the operational amplifier 3 through the resistor 5 and a static capacitance of the sensor S, respectively. An output of the operational amplifier 3 is connected to the output terminal 2 and to the inverting input terminal through the resistor 4. The non-inverting input terminal is grounded through the switch 6.
In the detection circuit of FIG. 1, the switch 6 is closed during an initialization period to charge the sensor capacitance to the voltage Vin supplied to the input terminal 1, and is opened when a measurement of the sensor capacitance is made. During the opening state of the switch 6, since the capacitance of the sensor S is connected to the non-inverting input terminal of a high input impedance, the charge accumulated on the capacitance is not discharged. On the other hand, as a physical change is applied to the sensor S by varying pressure to the diaphragm forming the sensor S, for instance, the static capacitance of the sensor S changes, causing a change in a voltage across the sensor capacitance. This voltage change is amplified by the operational amplifier 3, a gain of which is determined by the resistors 4 and 5, and appears at the output terminal 2.
In supplementing the foregoing description using equations, it should be assumed that resistances of the resistors 4 and 5 are Rf and Ri, the original static capacitance of the sensor S is Cs, and voltages at the non-inverting and inverting input terminals of the operational amplifier 3 are v.sup.+ and v.sup.-, respectively. Now, when the switch 6 is closed, the output voltage Vout is expressed by the following equation: EQU Vout=-Vin*Rf/Ri (1)
Assuming that the sensor capacitance changes from Cs to Cs' and the output voltage of the operational amplifier 3 changes from Vout to Vout' after the switch 6 is opened for measurement, Vout' is represented as follows: EQU Vout'={1+[1+(Rf/Ri)](Cs/Cs')}*Vin (2)
Here, with EQU Vout'-Vout=.DELTA.V, and Cs'-Cs=.DELTA.Cs, .DELTA.V=[1+(Rf/Ri)]* .DELTA.Cs/(Cs+.DELTA.Cs)*Vin (3)
is satisfied between .DELTA.V and .DELTA.Cs.
As mentioned above, since the output voltage Vout varies in response to the gain of the amplifier (that is the ratio Rf/Ri of the resistors 4 and 5) as well as the sensor capacitance Cs, it is not necessary to apply a high voltage as the input voltage Vin to the sensor capacitance.
With a low input voltage Vin, an electrostatic attractive force to the diaphragm may be relatively small. Therefore, the detection circuit shown in FIG. 1 may solve the problem that the electrode comes in contact with the diaphragm due to the electrostatic attractive force.